The ulimate package for correlations (by easystats)

The correlation package

The easystats project continues to grow with its more recent addition, a package devoted to correlations. Check-out its webpage here!

It’s lightweight, easy to use, and allows for the computation of many different kinds of correlations, such as partial correlations, Bayesian correlations, multilevel correlations, polychoric correlations, biweight, percentage bend or Sheperd’s Pi correlations (types of robust correlation), distance correlation (a type of non-linear correlation) and more, also allowing for combinations between them (for instance, Bayesian partial multilevel correlation).

You can install and load the package as follows:

``````install.packages("correlation")
library(correlation)``````

Examples

The main function is `correlation()`, which builds on top of `cor_test()` and comes with a number of possible options.

Correlation details and matrix

``````cor <- correlation(iris)
cor``````
``````## Parameter1   |   Parameter2 |     r |         95% CI | t(148) |      p |  Method | n_Obs
## ----------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.12 | [-0.27,  0.04] |  -1.44 | 0.152  | Pearson |   150
## Sepal.Length | Petal.Length |  0.87 | [ 0.83,  0.91] |  21.65 | < .001 | Pearson |   150
## Sepal.Length |  Petal.Width |  0.82 | [ 0.76,  0.86] |  17.30 | < .001 | Pearson |   150
## Sepal.Width  | Petal.Length | -0.43 | [-0.55, -0.29] |  -5.77 | < .001 | Pearson |   150
## Sepal.Width  |  Petal.Width | -0.37 | [-0.50, -0.22] |  -4.79 | < .001 | Pearson |   150
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] |  43.39 | < .001 | Pearson |   150
##
## p-value adjustment method: Holm (1979)``````

The output is not a square matrix, but a (tidy) dataframe with all correlations tests per row. One can also obtain a matrix using:

``summary(cor)``
``````## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |     0.82*** |      0.87*** |       -0.12
## Sepal.Width  |    -0.37*** |     -0.43*** |
## Petal.Length |     0.96*** |              |``````

Note that one can also obtain the full, square and redundant matrix using:

``as.table(cor)``
``````## Parameter    | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width
## ----------------------------------------------------------------------
## Sepal.Length |      1.00*** |       -0.12 |      0.87*** |     0.82***
## Sepal.Width  |        -0.12 |     1.00*** |     -0.43*** |    -0.37***
## Petal.Length |      0.87*** |    -0.43*** |      1.00*** |     0.96***
## Petal.Width  |      0.82*** |    -0.37*** |      0.96*** |     1.00***``````

Grouped dataframes

The function also supports stratified correlations, all within the tidyverse workflow!

``````library(dplyr)

iris %>%
select(Species, Petal.Width, Sepal.Length, Sepal.Width) %>%
group_by(Species) %>%
correlation()``````
``````## Group      |   Parameter1 |   Parameter2 |    r |        95% CI | t(48) |      p |  Method | n_Obs
## --------------------------------------------------------------------------------------------------
## setosa     |  Petal.Width | Sepal.Length | 0.28 | [ 0.00, 0.52] |  2.01 | 0.101  | Pearson |    50
## setosa     |  Petal.Width |  Sepal.Width | 0.23 | [-0.05, 0.48] |  1.66 | 0.104  | Pearson |    50
## setosa     | Sepal.Length |  Sepal.Width | 0.74 | [ 0.59, 0.85] |  7.68 | < .001 | Pearson |    50
## versicolor |  Petal.Width | Sepal.Length | 0.55 | [ 0.32, 0.72] |  4.52 | < .001 | Pearson |    50
## versicolor |  Petal.Width |  Sepal.Width | 0.66 | [ 0.47, 0.80] |  6.15 | < .001 | Pearson |    50
## versicolor | Sepal.Length |  Sepal.Width | 0.53 | [ 0.29, 0.70] |  4.28 | < .001 | Pearson |    50
## virginica  |  Petal.Width | Sepal.Length | 0.28 | [ 0.00, 0.52] |  2.03 | 0.048  | Pearson |    50
## virginica  |  Petal.Width |  Sepal.Width | 0.54 | [ 0.31, 0.71] |  4.42 | < .001 | Pearson |    50
## virginica  | Sepal.Length |  Sepal.Width | 0.46 | [ 0.20, 0.65] |  3.56 | 0.002  | Pearson |    50
##
## p-value adjustment method: Holm (1979)``````

Bayesian Correlations

It is very easy to switch to a Bayesian framework.

``correlation(iris, bayesian=TRUE)``
``````## Parameter1   |   Parameter2 |   rho |         95% CI |     pd | % in ROPE |     BF |         Prior |           Method | n_Obs
## -----------------------------------------------------------------------------------------------------------------------------
## Sepal.Length |  Sepal.Width | -0.11 | [-0.25,  0.02] | 90.77% |    44.17% |  0.509 | Beta (3 +- 3) | Bayesian Pearson |   150
## Sepal.Length | Petal.Length |  0.86 | [ 0.83,  0.89] |   100% |        0% | > 1000 | Beta (3 +- 3) | Bayesian Pearson |   150
## Sepal.Length |  Petal.Width |  0.80 | [ 0.76,  0.85] |   100% |        0% | > 1000 | Beta (3 +- 3) | Bayesian Pearson |   150
## Sepal.Width  | Petal.Length | -0.41 | [-0.52, -0.30] |   100% |        0% | > 1000 | Beta (3 +- 3) | Bayesian Pearson |   150
## Sepal.Width  |  Petal.Width | -0.35 | [-0.47, -0.24] |   100% |     0.02% | > 1000 | Beta (3 +- 3) | Bayesian Pearson |   150
## Petal.Length |  Petal.Width |  0.96 | [ 0.95,  0.97] |   100% |        0% | > 1000 | Beta (3 +- 3) | Bayesian Pearson |   150``````

Tetrachoric, Polychoric, Biserial, Biweight…

The `correlation` package also supports different types of methods, which can deal with correlations between factors!

``correlation(iris, include_factors = TRUE, method = "auto")``
``````## Parameter1         |         Parameter2 |     r |         95% CI | t(148) |      p |         Method | n_Obs
## -----------------------------------------------------------------------------------------------------------
## Sepal.Length       |        Sepal.Width | -0.12 | [-0.27,  0.04] |  -1.44 | 0.452  |        Pearson |   150
## Sepal.Length       |       Petal.Length |  0.87 | [ 0.83,  0.91] |  21.65 | < .001 |        Pearson |   150
## Sepal.Length       |        Petal.Width |  0.82 | [ 0.76,  0.86] |  17.30 | < .001 |        Pearson |   150
## Sepal.Length       |     Species.setosa | -0.72 | [-0.79, -0.63] | -12.53 | < .001 | Point-biserial |   150
## Sepal.Length       | Species.versicolor |  0.08 | [-0.08,  0.24] |   0.97 | 0.452  | Point-biserial |   150
## Sepal.Length       |  Species.virginica |  0.64 | [ 0.53,  0.72] |  10.08 | < .001 | Point-biserial |   150
## Sepal.Width        |       Petal.Length | -0.43 | [-0.55, -0.29] |  -5.77 | < .001 |        Pearson |   150
## Sepal.Width        |        Petal.Width | -0.37 | [-0.50, -0.22] |  -4.79 | < .001 |        Pearson |   150
## Sepal.Width        |     Species.setosa |  0.60 | [ 0.49,  0.70] |   9.20 | < .001 | Point-biserial |   150
## Sepal.Width        | Species.versicolor | -0.47 | [-0.58, -0.33] |  -6.44 | < .001 | Point-biserial |   150
## Sepal.Width        |  Species.virginica | -0.14 | [-0.29,  0.03] |  -1.67 | 0.392  | Point-biserial |   150
## Petal.Length       |        Petal.Width |  0.96 | [ 0.95,  0.97] |  43.39 | < .001 |        Pearson |   150
## Petal.Length       |     Species.setosa | -0.92 | [-0.94, -0.89] | -29.13 | < .001 | Point-biserial |   150
## Petal.Length       | Species.versicolor |  0.20 | [ 0.04,  0.35] |   2.51 | 0.066  | Point-biserial |   150
## Petal.Length       |  Species.virginica |  0.72 | [ 0.63,  0.79] |  12.66 | < .001 | Point-biserial |   150
## Petal.Width        |     Species.setosa | -0.89 | [-0.92, -0.85] | -23.41 | < .001 | Point-biserial |   150
## Petal.Width        | Species.versicolor |  0.12 | [-0.04,  0.27] |   1.44 | 0.452  | Point-biserial |   150
## Petal.Width        |  Species.virginica |  0.77 | [ 0.69,  0.83] |  14.66 | < .001 | Point-biserial |   150
## Species.setosa     | Species.versicolor | -0.88 | [-0.91, -0.84] | -22.43 | < .001 |    Tetrachoric |   150
## Species.setosa     |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.43 | < .001 |    Tetrachoric |   150
## Species.versicolor |  Species.virginica | -0.88 | [-0.91, -0.84] | -22.43 | < .001 |    Tetrachoric |   150
##
## p-value adjustment method: Holm (1979)``````

Partial Correlations

It also supports partial correlations:

``````iris %>%
correlation(partial = TRUE) %>%
summary()``````
``````## Parameter    | Petal.Width | Petal.Length | Sepal.Width
## -------------------------------------------------------
## Sepal.Length |    -0.34*** |      0.72*** |     0.63***
## Sepal.Width  |     0.35*** |     -0.62*** |
## Petal.Length |     0.87*** |              |``````

Gaussian Graphical Models (GGMs)

Such partial correlations can also be represented as Gaussian graphical models, an increasingly popular tool in psychology:

``````library(see) # for plotting
library(ggraph) # needs to be loaded

mtcars %>%
correlation(partial = TRUE) %>%
plot()``````

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